An exponential Diophantine equation involving Narayana cow’s numbers

Authors

  • Abdelkader HAMTAT

Keywords:

Padovan numbers, Narayana cow’s numbers, Linear form in logarithms, Reduction method.

Abstract

Let (Cn)n≤0 be the Narayana cow‘s sequence given by C0 = Cfi = C2 = fi and Cn‡3 = Cn‡2 ‡ Cn for n ≤ O. In this paper, we are interested in finding all powers of two which are sums of two Narayana cow‘s numbers, i.e.,
we detemine all solutions of the exponential Diophantine equation Cm ‡ Cn = Xs in nonnegative integers n, m, and s ≤ X.

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Published

2023-01-25

How to Cite

Abdelkader HAMTAT. (2023). An exponential Diophantine equation involving Narayana cow’s numbers. Utilitas Mathematica, 120, 37–48. Retrieved from https://utilitasmathematica.com/index.php/Index/article/view/1566

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